OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
Proves Chai's invariant-ideal conjecture for Lubin–Tate deformation rings over finite residue fields, at every prime and positive height n. Through the implication of Barthel–Heard–Naumann, this proves the Hovey–Strickland conjecture: dualizable K(n)-local spectra have exactly n+2 thick tensor ideals, and their Balmer spectrum is a chain of n+1 points.
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MANUSCRIPT 01
Stabilizer orbits and thick tensor ideals of dualizable K(n)-local spectra
We classify the prime and radical ideals of the Lubin–Tate deformation ring invariant under an open Morava stabilizer subgroup, at every prime and positive height. This proves Chai's invariant-ideal conjecture in the standard finite-residue-field formulation. It also proves the Hovey–Strickland conjecture: the dualizable…
Full source abstract
We classify the prime and radical ideals of the Lubin–Tate deformation ring invariant under an open Morava stabilizer subgroup, at every prime and positive height. This proves Chai's invariant-ideal conjecture in the standard finite-residue-field formulation. It also proves the Hovey–Strickland conjecture: the dualizable K(n)-local category has exactly n+2 thick tensor ideals, and its Balmer spectrum is a chain of n+1 points.
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